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Pramod Kumar Singh - One of the best experts on this subject based on the ideXlab platform.
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hybrid Dimension Reduction by integrating feature selection with feature extraction Method for text clustering
Expert Systems With Applications, 2015Co-Authors: Kusum Kumari Bharti, Pramod Kumar SinghAbstract:A novel hybrid Dimension Reduction Method is proposed.It obtains a highly informed and much reduced feature subset.It improves obtained results of the underlying clustering Method.It improves computational complexity of the underlying clustering Method. High Dimensionality of the feature space is one of the major concerns owing to computational complexity and accuracy consideration in the text clustering. Therefore, various Dimension Reduction Methods have been introduced in the literature to select an informative subset (or sublist) of features. As each Dimension Reduction Method uses a different strategy (aspect) to select a subset of features, it results in different feature sublists for the same dataset. Hence, a hybrid approach, which encompasses different aspects of feature relevance altogether for feature subset selection, receives considerable attention. Traditionally, union or intersection is used to merge feature sublists selected with different Methods. The union approach selects all features and the intersection approach selects only common features from considered features sublists, which leads to increase the total number of features and loses some important features, respectively. Therefore, to take the advantage of one Method and lessen the drawbacks of other, a novel integration approach namely modified union is proposed. This approach applies union on selected top ranked features and applies intersection on remaining features sublists. Hence, it ensures selection of top ranked as well as common features without increasing Dimensions in the feature space much. In this study, feature selection Methods term variance (TV) and document frequency (DF) are used for features' relevance score computation. Next, a feature extraction Method principal component analysis (PCA) is applied to further reduce Dimensions in the feature space without losing much information. The effectiveness of the proposed Method is tested on three benchmark datasets namely Reuters-21,578, Classic4, and WebKB. The obtained results are compared with TV, DF, and variants of the proposed hybrid Dimension Reduction Method. The experimental studies clearly demonstrate that our proposed Method improves clustering accuracy compared to the competitive Methods.
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a three stage unsupervised Dimension Reduction Method for text clustering
Journal of Computational Science, 2014Co-Authors: Kusum Kumari Bharti, Pramod Kumar SinghAbstract:Feature selection is widely used in text clustering to reduce Dimensions in the feature space. In this paper, we study and propose two-stage unsupervised feature selection Methods to determine a subset of relevant features to improve accuracy of the underlying algorithm. We experiment with hybrid approach of feature selection—feature selection (FS–FS) and feature selection—feature extraction (FS–FE) Methods. Initially, each feature in the document is scored on the basis of its importance for the clustering using two different feature selection Methods individually Mean-Median (MM) and Mean Absolute Difference (MAD).In the second stage, in two different experiments, we hybridize them with a feature selection Method absolute cosine (AC) and a feature extraction Method principal component analysis (PCA) to further reduce the Dimensions in the feature space. We perform comprehensive experiments to compare FS, FS–FS and FS–FE using k-mean clustering on Reuters-21578 dataset. The experimental results show that the two-stage feature selection Methods are more effective to obtain good quality results by the underlying clustering algorithm. Additionally, we observe that FS–FE approach is superior to FS–FS approach.
Kusum Kumari Bharti - One of the best experts on this subject based on the ideXlab platform.
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hybrid Dimension Reduction by integrating feature selection with feature extraction Method for text clustering
Expert Systems With Applications, 2015Co-Authors: Kusum Kumari Bharti, Pramod Kumar SinghAbstract:A novel hybrid Dimension Reduction Method is proposed.It obtains a highly informed and much reduced feature subset.It improves obtained results of the underlying clustering Method.It improves computational complexity of the underlying clustering Method. High Dimensionality of the feature space is one of the major concerns owing to computational complexity and accuracy consideration in the text clustering. Therefore, various Dimension Reduction Methods have been introduced in the literature to select an informative subset (or sublist) of features. As each Dimension Reduction Method uses a different strategy (aspect) to select a subset of features, it results in different feature sublists for the same dataset. Hence, a hybrid approach, which encompasses different aspects of feature relevance altogether for feature subset selection, receives considerable attention. Traditionally, union or intersection is used to merge feature sublists selected with different Methods. The union approach selects all features and the intersection approach selects only common features from considered features sublists, which leads to increase the total number of features and loses some important features, respectively. Therefore, to take the advantage of one Method and lessen the drawbacks of other, a novel integration approach namely modified union is proposed. This approach applies union on selected top ranked features and applies intersection on remaining features sublists. Hence, it ensures selection of top ranked as well as common features without increasing Dimensions in the feature space much. In this study, feature selection Methods term variance (TV) and document frequency (DF) are used for features' relevance score computation. Next, a feature extraction Method principal component analysis (PCA) is applied to further reduce Dimensions in the feature space without losing much information. The effectiveness of the proposed Method is tested on three benchmark datasets namely Reuters-21,578, Classic4, and WebKB. The obtained results are compared with TV, DF, and variants of the proposed hybrid Dimension Reduction Method. The experimental studies clearly demonstrate that our proposed Method improves clustering accuracy compared to the competitive Methods.
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a three stage unsupervised Dimension Reduction Method for text clustering
Journal of Computational Science, 2014Co-Authors: Kusum Kumari Bharti, Pramod Kumar SinghAbstract:Feature selection is widely used in text clustering to reduce Dimensions in the feature space. In this paper, we study and propose two-stage unsupervised feature selection Methods to determine a subset of relevant features to improve accuracy of the underlying algorithm. We experiment with hybrid approach of feature selection—feature selection (FS–FS) and feature selection—feature extraction (FS–FE) Methods. Initially, each feature in the document is scored on the basis of its importance for the clustering using two different feature selection Methods individually Mean-Median (MM) and Mean Absolute Difference (MAD).In the second stage, in two different experiments, we hybridize them with a feature selection Method absolute cosine (AC) and a feature extraction Method principal component analysis (PCA) to further reduce the Dimensions in the feature space. We perform comprehensive experiments to compare FS, FS–FS and FS–FE using k-mean clustering on Reuters-21578 dataset. The experimental results show that the two-stage feature selection Methods are more effective to obtain good quality results by the underlying clustering algorithm. Additionally, we observe that FS–FE approach is superior to FS–FS approach.
Ikjin Lee - One of the best experts on this subject based on the ideXlab platform.
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Selective Dimension Reduction Method (DRM) to enhance accuracy and efficiency of most probable point (MPP)–based DRM
Structural and Multidisciplinary Optimization, 2019Co-Authors: Jeong Woo Park, Hyunkyoo Cho, Ikjin LeeAbstract:To perform reliability-based design optimization (RBDO) in engineering systems, reliability analysis is required to calculate probability of failure ( P _ F ) for each performance function. Most probable point (MPP)–based Dimensional Reduction Method (DRM) has been developed to accurately estimate P _ F using the Gaussian quadrature integration Method. However, the existing MPP-based DRM is computationally expensive for highly nonlinear and/or high Dimensional problems since it needs to increase the number of integration points in all directions to guarantee accuracy. In the proposed Method, three statistical model selection Methods—Akaike information criterion (AIC), AIC correction (AICc), and Bayesian information criterion (BIC)—are utilized to identify characteristic of performance functions for more efficient integration point allocation. Then, genetic algorithm and simplex optimization Method are used to find the best models with the smallest AIC, AICc, and BIC values. No additional function evaluations are required for the model selection process since MPP candidate points are utilized. The best models obtained through optimization show where to allocate integration points which makes it possible not to allocate unnecessary integration points. Numerical study verifies that the proposed Method can guide how to allocate integration points according to characteristic of performance functions: no integration points for almost linear performance functions, minimal additional integration points for mildly nonlinear performance functions, and more integration points for highly nonlinear functions.
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Accuracy improvement of the most probable point-based Dimension Reduction Method using the hessian matrix
International Journal for Numerical Methods in Engineering, 2016Co-Authors: Seong Bin Kang, Jeong Woo Park, Ikjin LeeAbstract:Summary This paper proposes a most probable point (MPP)-based Dimension Reduction Method (DRM) using the Hessian matrix called HeDRM to improve accuracy of reliability analysis in existing MPP-based DRM Methods. Conventional MPP-based DRMs contain two types of errors: (1) error due to eliminating cross-terms of a performance function by using the univariate DRM; (2) error because of dependency of an axis direction after a rotational transformation. The proposed Method minimizes the aforementioned errors by utilizing the Hessian matrix of a performance function. By performing an orthogonal transformation using the eigenvectors of the Hessian matrix, the cross-term effect of the performance function is minimized and the axis direction that results in the most accurate calculation is obtained because the Gaussian quadrature points for numerical integration are arranged along the eigenvector directions. In this way, the error incurred by exiting MPP-based DRMs can be reduced that leads to more accurate probability of failure estimation. In addition, this paper proposes to allocate the Gaussian quadrature points using the magnitude of the eigenvalues of the Hessian matrix. This allocation makes it possible to predetermine the number of function evaluations required to estimate the probability of failure accurately and efficiently. Copyright © 2016 John Wiley & Sons, Ltd.
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sequential optimization and reliability assessment based on Dimension Reduction Method for accurate and efficient reliability based design optimization
Journal of Mechanical Science and Technology, 2015Co-Authors: Jongmin Lim, Byung Chai Lee, Ikjin LeeAbstract:This study develops an efficient and accurate Methodology for reliability-based design optimization (RBDO) by combining the most probable point (MPP)-based Dimension Reduction Method (DRM) to enhance accuracy and the sequential optimization and reliability assessment (SORA) to enhance efficiency. In many researches, first-order reliability Method (FORM) has been utilized for RBDO Methods due to its efficiency and simplicity. However, it might not be accurate enough for highly nonlinear performance functions. Therefore, the MPP-based DRM is introduced for the accurate reliability assessment in this study. Even though the MPP-based DRM significantly improves the accuracy, additional computations for the moment-based integration are required. It is desirable to reduce the number of reliability analyses in the RBDO process. Since decoupled approaches such as SORA reduce necessary reliability analyses considerably, DRM-based SORA is proposed in this study for accurate and efficient RBDO. Furthermore, convex linearization is introduced to approximate inactive probabilistic constraints to additionally improve the efficiency. The efficiency and accuracy of the proposed Method are verified through numerical examples.
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Reduction of ordering effect in reliability based design optimization using Dimension Reduction Method
AIAA ISSMO Multidisciplinary Analysis and Optimization Conference, 2009Co-Authors: Yoojeong Noh, Kyung K. Choi, Ikjin LeeAbstract:In reliability-based design optimization problems with correlated input variables, a joint cumulative distribution function needs to be used to transform the correlated input variables into independent standard Gaussian variables for the inverse reliability analysis. To obtain a true joint cumulative distribution function, a very large number of data (if not infinite) needs to be used, which is impractical in industry applications. In this paper, a copula is proposed to model the joint cumulative distribution function using marginal cumulative distribution functions and correlation parameters obtained from samples. Using the joint cumulative distribution function modeled by the copula, the transformation and the first-order reliability Method can be carried out. However, the first-order reliability Method may yield different reliability analysis results for different transformation ordering of input variables. Thus, the most probable-point-based Dimension Reduction Method, which is more accurate than the first-order reliability Method and more efficient than the second-order reliability Method, is proposed for the inverse reliability analysis to reduce the effect of transformation ordering.
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A New Inverse Reliability Analysis Method Using MPP-Based Dimension Reduction Method (DRM)
Volume 6: 33rd Design Automation Conference Parts A and B, 2007Co-Authors: Ikjin Lee, Kyung K. Choi, David GorsichAbstract:There are two commonly used reliability analysis Methods of analytical Methods: linear approximation - First Order Reliability Method (FORM), and quadratic approximation - Second Order Reliability Method (SORM), of the performance functions. The reliability analysis using FORM could be acceptable for mildly nonlinear performance functions, whereas the reliability analysis using SORM is usually necessary for highly nonlinear performance functions of multi-variables. Even though the reliability analysis using SORM may be accurate, it is not desirable to use SORM for probability of failure calculation since SORM requires the second-order sensitivities. Moreover, the SORM-based inverse reliability analysis is very difficult to develop. This paper proposes a Method that can be used for multi-Dimensional highly nonlinear systems to yield very accurate probability of failure calculation without requiring the second order sensitivities. For this purpose, the univariate Dimension Reduction Method (DRM) is used. A three-step computational process is proposed to carry out the inverse reliability analysis: constraint shift, reliability index (β) update, and the most probable point (MPP) approximation Method. Using the three steps, a new DRM-based MPP is obtained, which computes the probability of failure of the performance function more accurately than FORM and more efficiently than SORM.Copyright © 2007 by ASME
Lucy Xia - One of the best experts on this subject based on the ideXlab platform.
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QUADRO: A supervised Dimension Reduction Method via Rayleigh quotient optimization
Annals of statistics, 2015Co-Authors: Jianqing Fan, Han Liu, Lucy XiaAbstract:We propose a novel Rayleigh quotient based sparse quadratic Dimension Reduction Method - named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization) - for analyzing high- Dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-Dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating nonpolynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian Method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.
Alfredo H.-s. Ang - One of the best experts on this subject based on the ideXlab platform.
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Adaptive estimation for statistical moments of response based on the exact Dimension Reduction Method in terms of vector
Mechanical Systems and Signal Processing, 2019Co-Authors: Runyu Liu, Wenliang Fan, Yule Wang, Alfredo H.-s. AngAbstract:Abstract Obtaining the statistical moments of system responses remains one of the main topics of stochastic analysis. This paper presents a new adaptive point estimate Method (PEM) based on the exact Dimension Reduction Method in terms of vector. Firstly, the rigorous and exact Dimension Reduction Method in terms of vector is derived theoretically. Secondly, by introducing the nonnormal-to-normal transformation, the original variables are transformed into independent standard normal variables which are classified into several sub-vectors based on the delineation of the cross terms, and then the response moments can be described by an explicit function of the moments of multiple component functions. Thirdly, by combining with the two different approaches for estimating the moments of component sub-vector function, an adaptive PEM based on the exact Dimension Reduction Method in terms of vector, which comprises two sub-Methods, is proposed. Finally, several examples illustrate the accuracy and efficiency of the proposed Method.
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a new point estimation Method for statistical moments based on Dimension Reduction Method and direct numerical integration
Applied Mathematical Modelling, 2018Co-Authors: Wenliang Fan, Runyu Liu, Alfredo H.-s. AngAbstract:Abstract Estimation of statistical moments of structural response is one of the main topics for analysis of random systems. The balance between accuracy and efficiency remains a challenge. After investigating of the existing point estimation Method (PEM), a new point estimate Method based on the Dimension-Reduction Method (DRM) is presented. By introducing transformations, a system with general variables is transformed into the one with independent variables. Then, the existing PEMs based on the DRMs are investigated. Based on the qualitative analysis of difference in the approximations for response function and moment function, a new PEM is proposed, in which the response function is decomposed directly and the moments are calculated by high Dimensional integral directly. Compared with the existing PEM based on univariate DRM, the proposed Method is more friendly and easier to implement without loss of accuracy and efficiency; as compared with the PEM based on the generalized DRM, the proposed Method is of better precision at the cost of nearly the same efficiency and computational complexity, further, it does hold that the even-order moments are nonnegative. Finally, several examples are investigated to verify the performance of the new Method.